The cooling of a heat-generating board inside a parallel-plate channel

This paper addresses the fundamental question of how to position a heat-generating board inside a parallel-plate channel, where it is cooled by forced convection. It is shown that when the board substrate is a relatively good thermal conductor, the best board position is near one of the channel walls, and the worst position is in the middle of the channel. The best and worst positions switch places when the board substrate is a relatively poor conductor. The optimal spacing between a heat-generating surface (uniform temperature, or uniform heat flux) and the insulated wall that completes a parallel-plate channel is reported. Finally, it is shown under what conditions it is advantageous to divide a heat-generating board into two or more equidistant boards inside the same channel, when the total rate of heat generation of all the boards and the channel spacing are fixed.